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One corollary of E=mc^2 is that the rest mass of a bound state of fundamental particles will not equal the sum of the rest masses of the individual constituents

One corollary of E=mc^2 is that the rest mass of a bound state of fundamental particles will not equal the sum of the rest masses of the individual constituents. For example, the rest mass of a Helium-4 nucleus turns out to be less than the sum of the rest masses of the four nucleons of which it is composed. The difference is only about 0.7% but is famously quite a lot of energy when interpreted using E=mc^2. It's a lot more fun if we go one level down though: protons are far HEAVIER than the sum of their constituents. Apparently almost 99% of the rest mass of a proton is the binding energy of the zero-rest-mass gluons that hold their three quarks together. I think it's fun that the vast majority of the mass of ordinary matter, of which we are all constituted, is best explained as gluon binding energy via E=mc^2.

cohomologo 9y ago
I think you've got that last part backwards. When you have constituents with binding energy, that reduces the total energy of the system and reduces the mass. So it seems that the mass of the proton is quark mass + gluon kinetic energy - bonding energy, and most of the mass comes from gluon kinetic energy.
- ocfnash 9y ago
  Yes I do indeed; thank you for the correction!
- hjaved 9y ago
  Thank you. Would like to understand that why does having constituents with binding energy reduce the total energy of the system instead of adding to it?
  - davrosthedalek 9y ago
    You have to think about it the other way around: The constituents don't have binding energy. That energy becomes available when you let them bind, and you have to pay it back if you want to unbind them. Example: If you have a proton and an electron, making a hydrogen atom will release about 13.6 eV (if it goes to the lowest energy state). You have to spend that 13.6eV to ionize the hydrogen, i.e. to get the electron far away from the proton again.
danbruc 9y ago
I am not a physicist, but isn't all mass just energy if you just dig deep enough? As far as I know there is nothing that has [some] mass that is not ultimately explained as kinetic or potential energy.
davrosthedalek 9y ago
It's a little bit tricky with the protons, as free quarks don't exist. One could argue that the mass of free quarks is infinite, which explains hadronization: it is energetically cheaper to produce quarks out of nothing so that the quarks are not free. What is certainly true is that, writing down the QCD Lagrangian, there is nothing which tells you the scale of the proton mass, nor the somewhat different scale of the pion mass. This is in sharp contrast to the Hydrogen case, where the masses which appear in the Lagrangian are very close to the total mass of the Hydrogen.

cohomologo 9y ago

I think you've got that last part backwards. When you have constituents with binding energy, that reduces the total energy of the system and reduces the mass. So it seems that the mass of the proton is quark mass + gluon kinetic energy - bonding energy, and most of the mass comes from gluon kinetic energy.

ocfnash 9y ago
Yes I do indeed; thank you for the correction!
hjaved 9y ago
Thank you. Would like to understand that why does having constituents with binding energy reduce the total energy of the system instead of adding to it?
- davrosthedalek 9y ago
  You have to think about it the other way around: The constituents don't have binding energy. That energy becomes available when you let them bind, and you have to pay it back if you want to unbind them. Example: If you have a proton and an electron, making a hydrogen atom will release about 13.6 eV (if it goes to the lowest energy state). You have to spend that 13.6eV to ionize the hydrogen, i.e. to get the electron far away from the proton again.

danbruc 9y ago

I am not a physicist, but isn't all mass just energy if you just dig deep enough? As far as I know there is nothing that has [some] mass that is not ultimately explained as kinetic or potential energy.

davrosthedalek 9y ago

It's a little bit tricky with the protons, as free quarks don't exist. One could argue that the mass of free quarks is infinite, which explains hadronization: it is energetically cheaper to produce quarks out of nothing so that the quarks are not free. What is certainly true is that, writing down the QCD Lagrangian, there is nothing which tells you the scale of the proton mass, nor the somewhat different scale of the pion mass. This is in sharp contrast to the Hydrogen case, where the masses which appear in the Lagrangian are very close to the total mass of the Hydrogen.